Precalculus Examples

$\frac{\log (0.1)}{\log (8)}$

Step 1

Log base $10$ of $0.1$ is approximately $- 1$ .

$\frac{- 1}{\log (8)}$

Step 2

Rewrite $\log (8)$ as $\log (2^{3})$ .

$\frac{- 1}{\log (2^{3})}$

Step 3

Expand $\log (2^{3})$ by moving $3$ outside the logarithm.

$\frac{- 1}{3 \log (2)}$

Step 4

Cancel the common factor of $- 1$ and $3$ .

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Step 4.1

Rewrite $- 1$ as $1 (- 1)$ .

$\frac{1 (- 1)}{3 \log (2)}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $1$ out of $3 \log (2)$ .

$\frac{1 (- 1)}{1 (3 \log (2))}$

Step 4.2.2

Cancel the common factor.

$\frac{1 \cdot - 1}{1 (3 \log (2))}$

Step 4.2.3

Rewrite the expression.

$\frac{- 1}{3 \log (2)}$

Step 5

Simplify $3 \log (2)$ by moving $3$ inside the logarithm.

$\frac{- 1}{\log (2^{3})}$

Step 6

Raise $2$ to the power of $3$ .

$\frac{- 1}{\log (8)}$

Step 7

Move the negative in front of the fraction.

$- \frac{1}{\log (8)}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$- \frac{1}{\log (8)}$

Decimal Form:

$- 1.10730936 \dots$